Assume that the interest rate is 3.16% for all maturities (flat term structure). Compute the (Macaulay) duration and the modified duration of the following bonds:

A discount bond maturing in 18 years with a face value of $1,000.

Duration:

Modified Duration:

(b)

A perpetual bond paying an annual coupon $42.0 forever.

Duration:

Modified Duration:

(c)

A 5-year Treasury note with the face value of $100 and the annual coupon at the rate of 5.0%.

Duration:

Modified Duration: